>>574 補足 www.maths.ed.ac.uk/~aar/papers/exoticsmooth.pdf Exotic Smoothness and Physics Differential Topology and Spacetime Models 2007 より 11.2.4 Geometric structures on %manifolds and exotic differential structures
To summarize, we hope to have provided support for the conjecture: Conjecture: The differential structures on a simply-connected compact, 4-manifold M are determined by the homotopy classes [M, BGl(T)+] and by the algebraic K-theoy K3(T) where T is the hyperfinite II1 factor C*-algebra. The classes in K3(T) are given by the geometric structure and/or a codamension-1 foliation of a homology 3-sphere in M determining the Akbulut cork of M.
From the physical point of view, this conjecture is very interesting because it connects the abstract theory of differential structures with well-known structures in physics like operator algebras or bundle theory. Perhaps such speculations may provide a geometrization of quantum mechanics or more. We close this section, and book, which these highly conjectural remarks.
